What is the seventh term of the geometric sequence with a first term of 729 and a common ratio of ?

Answer:

About 6 athletes.

Step-by-step explanation:

We are concerned only with the percent of athletes that are above one standard deviation.

Between one standard deviation and two standard deviations, there is 13.6% of the athletes.

From 2 to 3, there is 2.1%. Above 3, there is 0.2%.

The sum of those percentages is 15.9% of 40 = 0.159 · 40 = 6.36 or about 6 athletes.

Hope this helps.

The solution is: About 6 athletes does that represent.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

We are concerned only with the percent of athletes that are above one standard deviation.

Between one standard deviation and two standard deviations, there is 13.6% of the athletes.

From 2 to 3, there is 2.1%. Above 3, there is 0.2%.

The sum of those percentages is 15.9% of 40

= 0.159 · 40

= 6.36 or about 6 athletes.

Hence, The solution is: About 6 athletes does that represent.

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Answer with Step-by-step explanation:

We are given that

[tex]f(x)=4x[/tex]

Interval=[2,5]

[tex]h=\frac{b-a}{n}=\frac{5-2}{n}=\frac{3}{n}[/tex]

[tex]x_i=i\frac{3}{n}[/tex]

Where i=1,2,3,... n

[tex]f(x_i)=4i\times \frac{3}{n}=\frac{12i}{n}[/tex]

Riemann sum=[tex]\lim_{n\rightarrow \infty}\sum_{i=1}^{n}f(x_i)\cdot h=\lim_{n\rightarrow \infty}\sum_{i=1}^{n}(\frac{12i}{n}\times \frac{3}{n}[/tex]

Riemann sum=[tex]\lim_{n\rightarrow \infty}\frac{36}{n^2}\sum_{i=1}^{n}i[/tex]

Riemann sum=[tex]\lim_{n\rightarrow \infty}\frac{36}{n^2}\times \frac{n(n+1)}{2}[/tex]

By using

[tex]\sum n=\frac{n(n+1)}{2}[/tex]

Riemann sum=[tex]\lim_{n\rightarrow \infty}\frac{18n(n+1)}{n^2}=\lim_{n\rightarrow \infty}18(1+\frac{1}{n})[/tex]

Apply the limit

Area under the curve=[tex]18[/tex] square units

The Riemann sum formula for [tex]\(f(x) = 4x\)[/tex] over [2, 5] using right-hand endpoints and n subintervals is [tex]\(R_n = \sum_{k=1}^{n} 4\left(2 + k \cdot \frac{3}{n}\right) \cdot \frac{3}{n}\)[/tex]. The area is obtained by taking the limit as n approaches infinity.

The Riemann sum for a function f(x) over the interval [a, b] using right-hand endpoints and dividing the interval into n subintervals is given by:

[tex]\[ R_n = \sum_{k=1}^{n} f(c_k) \Delta x \][/tex]

where [tex]\( c_k \)[/tex] is the right-hand endpoint of the [tex]\( k \)[/tex]-th subinterval, [tex]\( \Delta x \)[/tex] is the width of each subinterval, and [tex]\( n \)[/tex] is the number of subintervals.

For the function f(x) = 4x over the interval [2, 5], the width of each subinterval [tex]\( \Delta x \)[/tex] is given by:

[tex]\[ \Delta x = \frac{b - a}{n} \][/tex]

In this case, [tex]\( a = 2 \), \( b = 5 \), and \( f(x) = 4x \)[/tex]. Therefore:

Now, the right-hand endpoint [tex]\( c_k \)[/tex] for each subinterval is given by:

[tex]\[ c_k = a + k \Delta x \][/tex]

Substitute the values:

[tex]\[ c_k = 2 + k \cdot \frac{3}{n} \][/tex]

[tex]\[ \Delta x = \frac{5 - 2}{n} = \frac{3}{n} \][/tex]

Now, substitute these expressions into the Riemann sum formula:

[tex]\[ R_n = \sum_{k=1}^{n} f(c_k) \Delta x \][/tex]

[tex]\[ R_n = \sum_{k=1}^{n} 4(2 + k \cdot \frac{3}{n}) \cdot \frac{3}{n} \][/tex]

Simplify this expression. To find the area under the curve, take the limit as n approaches infinity:

[tex]\[ \lim_{n \to \infty} R_n \][/tex]

This limit will give you the area under the curve f(x) = 4x over the interval [2, 5].

To find the probability of getting all 4 cards that are queens, we calculate the number of favorable outcomes and the total number of possible outcomes. The probability is the number of favorable outcomes divided by the total number of possible outcomes.

To find the probability of getting all 4 cards that are queens, we need to calculate the number of favorable outcomes (4 queens) and the total number of possible outcomes when 4 cards are dealt from a shuffled deck of 52 cards.

The total number of possible outcomes can be calculated using combinations. We can use the formula C(n, r) = n! / (r!(n-r)!), where n is the total number of items (52 cards) and r is the number of items to be selected (4 cards). So, C(52,4) = 52! / (4!(52-4)!) = 270,725.

The number of favorable outcomes is 4 since we want all 4 cards to be queens.

Therefore, the probability is the number of favorable outcomes divided by the total number of possible outcomes: P(all 4 cards are queens) = 4/270,725 = 0.00001475 (rounded to 5 decimal places) or approximately 0.0015%.

Answer:

Step-by-step explanation:

Given that,

Rate of change of a function

1. From x = 1 to x = 4

2. From x = 5 to x =8

Then,

Rate of change for first condition

∆x/∆t = (x2-x1) / (t2-t1)

∆x/∆t = (4-1) / (t2-t1)

∆x/∆t = 3 / (t2-t1)

Rate of change for second condition

∆x/∆t = (x2-x1) / (t2-t1)

∆x/∆t = (8-5) / (t2-t1)

∆x/∆t = 3 / (t2-t1)

The rate of change are equal, it shows that the slope are equal.

So, it is a straight line function.

Since it has equal rate of change..

Answer:

Explanation:

The measure of the missing angle is [tex]25^\circ[/tex]. So, the first option is correct.

Important information:

We need to find the third angle of the triangle.

According to the angle sum property, the sum measure of all interior angles of a triangle is 180 degrees.

Let [tex]x[/tex] be the measure of the missing angle.

[tex]x+35^\circ+120^\circ=180^\circ[/tex]

[tex]x+155^\circ=180^\circ[/tex]

[tex]x=180^\circ-155^\circ[/tex]

[tex]x=25^\circ[/tex]

Thus, the first option is correct.

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Answer:

the density of copper is 90.03g/cm³

Step-by-step explanation:

This problem bothers on the density of a substance, this case for a copper material

Given data

Mass of copper m = 1355g

Volume of copper block v= l*b*h

10*5*3=150cm³

We know that the density

ρ= mass/volume

ρ= 1355/150

ρ= 90.03g/cm²

The density of a substance is defined as the mass of the substance per unit volume

Answer:

The answer is 8.9 gm/cm cubed

Step-by-step explanation:

Just did it on algebra nation

Answer:

It should take somewhere between 8 to 9 minutes to decay until there are 30 grams remaining.

It will take about 8 minutes until there are 30 grams of the element remaining.

percentage, a relative value indicating hundredth parts of any quantity.

we can use the formula for exponential decay:

[tex]N(t) = N_{0} e^(^-^k^t^)[/tex]

where:

N₀ is the initial quantity (in grams) of the element

N(t) is the quantity (in grams) of the element at time t

k is the decay constant

t is the time (in minutes)

We can start by finding the value of k, which is related to the percentage of decay per minute:

k = ln(1 - %/100)

= ln(1 - 30/100)

= -0.35667

Next, we can plug in the values we have and solve for t:

[tex]30 = 630.e^(^-^0^.^3^5^6^6^7^t^)[/tex]

Dividing both sides by 630, we get:

[tex]0.0476 = e^(^-^0^.^3^5^6^6^7^t^)[/tex]

Taking the natural logarithm of both sides, we get:

ln(0.0476) = -0.35667t

Solving for t, we get:

t = 7.75

Therefore, it will take about 8 minutes until there are 30 grams of the element remaining.

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Answer:

1/2 because cake are almost made out of the same thing pie are made of so they are using half of the intransigents to make cake and there using it to make pie

Step-by-step explanation:

Answer:

A. 2/7

Step-by-step explanation:

took the test on edg.2020

good luck :)

Answer:

The answer to your question is the letter A.

Step-by-step explanation:

Data

             y = x² + 10x + 26

Factor the right side of the equation

         y - 26 = x² + 10x

-Complete the perfect trinomial square

         y - 26 + (5)² =  x² + 10x + (5)²

-Simplify

        y - 26 + 25 = x² + 10x + 25

              y - 1 = (x + 5)²

Vertex = (-5 , 1)

The function given is a vertical parabola whose axis of symmetry goes through x = -5

Answer:

11/16 and 12/16=3/4

Step-by-step explanation:

First we need to get a common denominator

5/8*2/2 = 10/16

The fractions between 10/16 and 13/16

are 11/16 and 12/16

We can simplify 12/16 =6/8=3/4

There are many others if we go with a higher common denominator.  These are just two examples

$65×25%=$65×($65×0.25)=$1056.25

$823×21.4%=$823×($823×0.214)=$144,948.406

$33,333×4.3%=$33,333×($33,333×0.043)=$47,776,822.227

$12,831×52%=$12,831×($12,831×0.52)=$85,609,971.72

$44,893×3.4%=44,893×(44,893×0,034)=$68,522,969.266

Answer:

y+4(-1)=11

y=11+4

y=15.

ii)y+4(0)=11

y=11

ii)y+4(3)=11

y=11-12

y=-1

when y=1

1+4x=11

4x=11+1

4x=12

x=3

The total cost (excluding raw materials) of filling this order is $11,300.

Let's denote the matrices as follows:

[tex]\[ B = \begin{bmatrix} 400 \\ 200 \\ 350 \end{bmatrix} \][/tex]

This matrix represents the number of loaves for each type of bread.

[tex]\[ A = \begin{bmatrix} 14 & 25 & 2 \end{bmatrix} \][/tex]

This matrix represents the cost per hour for mixing, baking, and packaging.

[tex]\[ C = \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix} \][/tex]

This matrix represents the number of hours needed for each process (mixing, baking, packaging).

Now, we can calculate the product BAC to find the total cost:

[tex]\[ BAC = B \cdot A \cdot C \][/tex]

Let's perform the calculations:

[tex]\[ BAC = \begin{bmatrix} 400 \\ 200 \\ 350 \end{bmatrix} \begin{bmatrix} 14 & 25 & 2 \end{bmatrix} \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix} \][/tex]

[tex]\[ BAC = \begin{bmatrix} (400 \times 14 + 200 \times 25 + 350 \times 2) \end{bmatrix} \][/tex]

[tex]\[ BAC = \begin{bmatrix} 5600 + 5000 + 700 \end{bmatrix} \][/tex]

[tex]\[ BAC = \begin{bmatrix} 11300 \end{bmatrix} \][/tex]

So, the total cost (excluding raw materials) of filling this order is $11,300.

Answer:

Step-by-step explanation:

Given:

250 students And respective percentage of students who are having dogs and cats.

To Find:

60% said that they have a cat. Of the students who have a cat, 70% also have a dog. Of the students who do not have a cat, 75% have a dog

Solution:

Taking each condition as follows:

60% of 250 have cats

i.e   0.6 *250= 150 students have cats

So 150 students of that 70% has dogs

i.e 0.7*150=15*7=105 students have dogs

Now 40 % of 250 dont have cats

i.e  0.4*250=100 students dont have cats

So  Of which 75 % have dogs

i.e 0.75*100= 75 students will have dogs.

Now making tabular forms to understand properly,

(Refer the Attachment)

Answer:

The combined average length of five male elephants is 3750cm

Step-by-step explanation:

1 elephant = 7.5m

5 elephants=?

We cross multiply.

5 * 7.5= 37.5m

So the average combined length of 5 male elephants is 37.5m

So we convert 37.5m to centimetres

Recall, 100cm = 1m

With this in mind, we convert 37.5m to cm by multiplying by 100

So, 37.5 x 100= 3750cm.

The combined average length of five male African elephants is 3750 centimeters, obtained by converting the length of one elephant to centimeters and multiplying by five.

To calculate the combined average length, in centimeters, of five male African elephants, we start by converting the length of one elephant from meters to centimeters. Knowing that 1 meter is equivalent to 100 centimeters, we can find the length of one elephant in centimeters:

7.5 meters/elephant × 100 centimeters/meter = 750 centimeters/elephant

Now, to find the total length of five elephants:

750 centimeters/elephant × 5 elephants = 3750 centimeters

Therefore, the combined average length of five male African elephants is 3750 centimeters.

Answer:

153.1ml

Step-by-step explanation:

We have 12.5ml of acid in the solution.

If we want this to be 3% then we can divide this value by 3 and times by 100 to get the total value.

416.6ml total solution amount

415.6-12.5-250=153.1

Answer:

Inscribed angle

Step-by-step explanation:

an angle is a inscribed angle if the vertex is on a circle and the sides of the angle are chords of the the circle

Final answer:

An angle with its vertex on a circle and sides that are chords of the circle is called an inscribed angle. This concept relates to the angle of rotation, which is the arc length divided by the radius of the circle.

Explanation:

An angle with its vertex on a circle and sides that are chords of the circle is known as an inscribed angle. The angle is formed by the two chords that intersect on the circumference of the circle, creating an angle inside the circle.

To understand this concept in relation to movement along a circle's circumference, like a compact disc (CD), one can think of the movement in terms of the angle of rotation. For any point on a rotating CD, the rotation angle can be calculated. This angle is the ratio of the arc length (the distance traveled along the circumference) to the radius of the circle. If the CD completes one full revolution, this angle equals 2π radians (or 360 degrees), indicating a full rotation.

Understanding inscribed angles and rotation angles helps us think about geometric figures and rotational movement, whether in a mathematical problem or in a physical example like a CD rotating on its axis.

When you cross-multiply the fractions 2/5 and 3/8, you obtain two products: 16 and 15.

To find the products obtained when you cross-multiply the fractions 2/5 and 3/8, you multiply the numerator of the first fraction with the denominator of the second fraction, and the denominator of the first fraction with the numerator of the second fraction.

So, here are the steps:

Therefore, the two products you get when you cross-multiply the fractions 2/5 and 3/8 are 16 and 15. Thus, the correct answer is option c: 16 and 15.

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Answer:

36.87°

Step-by-step explanation:

Since ABC is a right-angle triangle, we can use trigonometric ratios to solve for unknown angles and sides.

For Angle at A, we have lengths of opposite and adjacent sides so we can use tangent at A.

tan(A) = opposite/adjacent

tan(A) = CB/AB

tan(A) = 6/8

A = (tan^-1)(0.75)

A = 36.86989765°

Answer:

Angle E should be 105 degrees.

Step-by-step explanation:

Since a triangle equals 180, you subtract 47° and 28° from that and come up with 105°.

The angle E is 105 degrees when  Angle D is 28 degrees. Angle F is 47 degrees.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Let the triangle be DEF.

Angle D is 28 degrees. Angle F is 47 degrees.

We need to find the angle E

By angle sum property we know the sum of three angles of a triangle is 180 degrees.

28+47+x=180

75+x=180

Subtract 75 from both sides

x=180-75

x=105 degrees.

Hence, the angle E is 105 degrees when  Angle D is 28 degrees. Angle F is 47 degrees.

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Answer:

The answer is D. x= 4

Step-by-step explanation:

The angles are congruent so

2.3x +25 = 5.8x + 11

2.3x - 5.8x = 11 - 25

-3.5x = -14

x = 14/3.5

x = 4.

Answer:

The answer to your question is the letter D.

Step-by-step explanation:

Data

First angle          2.3x + 25

Second angle    5.8x + 11

Process

1.- This angles are congruents, this menas that they measure the same so to find x, equal both values.

                         2.3x + 25 = 5.8x + 11

2.- Solve for x

                         2.3x - 5.8x = 11 - 25

3.- Simplification

                                -3.5x = -14

                                      x = -14/-3.5

4.- Result

                                     x = 4

Answer:

A) 18+81=9(x^2+6x+9)

D)11+(x+3)^2

Step-by-step explanation:

To solve this by completing the square, we want to get it to the form of: (x + 3)^2 = 9

There are multiple ways to get there.

First we could divide by 9 to get.

x^2 + 6x = 0

Then, add 9 to both sides to get:

x^2 + 6x + 9 = 9

Factor the left side:

(x + 3)^2 = 9

Now, you can solve this equation by completing the square.

(*I think you have a typo in your answer choices)

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Final answer:

The area of Ciro's trapezoidal sign is calculated using the formula for the area of a trapezoid, which is 503.5 square inches.

Explanation:

The student's question involves calculating the area of a trapezoid. The formula for the area of a trapezoid is ½(√ + ∛)×h, where √ and ∛ are the lengths of the parallel sides and h is the distance between these sides. Given that √ = 18 inches, ∛ = 35 inches, and h = 19 inches, plug these values into the formula to get:

Area = ½(18 inches + 35 inches) × 19 inches

Area = ½(53 inches) × 19 inches

Area = 26.5 inches × 19 inches

Area = 503.5 square inches

So, the area of Ciro's sign, which is trapezoidal is 503.5 square inches.

Answer:

(0,-5)

Step-by-step explanation:

(−2,−2)

and

(2,−8)

Midpoint: (-2+2)/2, (-2-8)/2

0/2, -10/2

(0,-5)

Answer

the absolute value of -2 is greater than the absolute value of 1.5

Step-by-step explanation:

the absolute value of -2 is 2 and the absolute value of 1.5 is 1.5  

The absolute value of -2 is 2, which is greater than 1.5. Therefore, this inequality is false.

The absolute value of -3.5 is 3.5, which is greater than 2.5. Therefore, this inequality is true.

From the information given, we have that;

|−2| < 1.5:

The absolute value of -2 is 2, which is greater than 1.5. Therefore, this inequality is false.

|−3.5| > 2.5:

The absolute value of -3.5 is 3.5, which is greater than 2.5. Therefore, this inequality is true.

Since we have an OR statement ("or"), if at least one of the inequalities is true, the entire statement is true.

In this case, only the second inequality is true.

Therefore, the overall statement is true.

The complete statement:

The absolute value ___-2__ < __1.5___ or ___-3.5 __ > _2.5______

Answer:

The nth term = n^2 - 2n - 3.

Step-by-step explanation:

                     -4 -3  0  5  12  21  32

Differences      1  3  5  7    9    11

Difference         2 2   2   2    2    <-- divide this by 2 so its n^2.

So the first term is n^2

List the original numbers  and values of n^2:

sequence   -4  -3  0   5    12    21   32

n^2               1    4  9   16  25   36   49

Subtract      -5  -7 -9  -11   -13   -15    -17

These last numbers have a common difference of -2 so the next part of the answer is -2n and get the  -5, -7 etc we add -3.

So our formula is n^2 - 2n - 3.

Check for the 3rd term:

3rd term is  3^2 - 2(3) - 3 = 0.

5th term = 5^2 - 2(5) - 3 =  25 - 10 - 3 = 12.

Simulate a true/false test by flipping a coin for each question with heads for 'true' and tails for 'false'. To select a homeroom representative from six students, assign numbers and use a random number generator or equivalent method for random selection.

To simulate the situation where you guess the answers on a true/false test with 20 questions, you could use a coin to represent the random guessing. Flip the coin 20 times where heads represents 'true' and tails represents 'false', recording the number of correct outcomes as needed. Since each question can only have one correct answer, the probability of getting a question right is 0.50.

For the situation where one student out of 6 is randomly chosen to be the homeroom representative, you could assign each of the six students a number from 1 to 6. Then, using a random number generator, die, or drawing numbers from a hat, you select a number at random to determine the representative. The probability of any one student being selected is [tex]\frac{1}{6}[/tex] or approximately 0.17.

Answer:

D

Step-by-step explanation:

100+25 * 12 ; 100+300 = 400 ; difference = 400-320=80 ; percent increase since it is 1 year = 80/320 =1/4=0.25 = 25/100=25%

Answer:

1 1/3 ft

Step-by-step explanation:

We have 8 feet of board to work with. In order to find how long each of the 6 pieces are, we need to divide 8 by 6: 8 / 6 = 4 / 3 = 1 1/3 ft.

Thus, the length of each piece is 1 1/3 ft.

Hope this helps!